Removing or making nasty spikes less audible?

There is a free plugin for Audaucity called Paul-L’s de-clicker which will do the job …

However it can take its time , ( e.g. processing time can be 10x playbacktime , depending on the setings ).

Brian Davies De-Click stand-alone software is much faster , but not free.
[ In some cases Paul-L’s de-clicker produces a better result ]